A Characterization of Global Entanglement

A Characterization of Global Entanglement We define a set of 2 n−1−1 entanglement monotones for n qubits and give a single measure of entanglement in terms of these. This measure is zero except on globally entangled (fully inseparable) states. This measure is compared to the Meyer–Wallach measure for two, three, and four qubits. We determine the four-qubit state, symmetric under exchange of qubit labels, which maximizes this measure. It is also shown how the elementary monotones may be computed as a function of observable quantities. We compute the magnitude of our measure for the ground state of the four-qubit superconducting experimental system investigated in [M. Grajcar et al., Phys. Rev. Lett. 96, 047006 (2006)], and thus confirm the presence of global entanglement in the ground state. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals
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Publisher
Kluwer Academic Publishers-Plenum Publishers
Copyright
Copyright © 2007 by Springer Science+Business Media, LLC
Subject
Physics; Characterization and Evaluation of Materials; Computer Science, general ; Engineering, general; Mathematics, general; Physics, general
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-007-0052-7
Publisher site
See Article on Publisher Site

Abstract

We define a set of 2 n−1−1 entanglement monotones for n qubits and give a single measure of entanglement in terms of these. This measure is zero except on globally entangled (fully inseparable) states. This measure is compared to the Meyer–Wallach measure for two, three, and four qubits. We determine the four-qubit state, symmetric under exchange of qubit labels, which maximizes this measure. It is also shown how the elementary monotones may be computed as a function of observable quantities. We compute the magnitude of our measure for the ground state of the four-qubit superconducting experimental system investigated in [M. Grajcar et al., Phys. Rev. Lett. 96, 047006 (2006)], and thus confirm the presence of global entanglement in the ground state.

Journal

Quantum Information ProcessingSpringer Journals

Published: May 15, 2007

References

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